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Theorem bd0 11203
Description: A formula equivalent to a bounded one is bounded. See also bd0r 11204. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd0.min BOUNDED 𝜑
bd0.maj (𝜑𝜓)
Assertion
Ref Expression
bd0 BOUNDED 𝜓

Proof of Theorem bd0
StepHypRef Expression
1 bd0.min . 2 BOUNDED 𝜑
2 bd0.maj . . 3 (𝜑𝜓)
32ax-bd0 11192 . 2 (BOUNDED 𝜑BOUNDED 𝜓)
41, 3ax-mp 7 1 BOUNDED 𝜓
Colors of variables: wff set class
Syntax hints:  wb 103  BOUNDED wbd 11191
This theorem was proved from axioms:  ax-mp 7  ax-bd0 11192
This theorem is referenced by:  bd0r  11204  bdth  11210  bdnth  11213  bdnthALT  11214  bdph  11229  bdsbc  11237  bdsnss  11252  bdcint  11256  bdeqsuc  11260  bdcriota  11262  bj-axun2  11294
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